Modified form of binary and ternary 3-point subdivision schemes

Binary 3-point scheme, developed by Hormann and Sabin [Hormann, K. and Sabin, Malcolm A., 2008, A family of subdivision schemes with cubic precision, Computer Aided Geometric Design, 25, 41-52], has been modified by introducing a tension parameter which generates a family of C¹ limiting curves for certain range of tension parameter. Ternary 3-point scheme, introduced by Siddiqi and Rehan [Siddiqi, Shahid S. and Rehan, K., 2009, A ternary three point scheme for curve designing, International Journal of Computer Mathematics, In Press, DOI: 10.1080/00207160802428220], has also been modified by introducing a tension parameter which generates family of C¹ and C² limiting curves for certain range of tension parameter. Laurent polynomial method is used to investigate the continuity of the subdivision schemes. The performance of modified schemes has been demonstrated by considering different examples along with its comparison with the established subdivision schemes.     

一种基于正则参数化的降维细分算法(英文)

In our previous work, we have given an algorithm for segmenting a simplex in the n-dimensional space into rt n＋ 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons. In this paper, we prove that the map F is a one to one correspondence at least in lower dimensional spaces （n _〈 3）. Moreover, we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular Bézier patches on a 2-dimensional space. Finally, we compare our schemes with Goldman＇s in computational complexity and speed.     

对流扩散方程的一种新型特征差分方法

利用在网格内恰当选取特征线上插值点的技巧,提出了一种新型的求解对流扩散方程的特征差分方法,并给出了稳定性与收敛性分析.该方法避免了数值扩散的产生,同时具有O(τ h~2)阶的收敛阶.数值实验表明,该方法是一个高效、稳定和收敛的数值方法.     

激光衍射测量中应用插值细分的可行性分析

激光衍射测微的精度关键在于衍射图样暗纹间距的精确测量，暗纹间距的测量目前主要采用高位数、小中心距的固体图象传感器线阵，为此，提出了一种硬件插值细分的方法。介绍了激光衍射的测量原理，分析了图像传感器的功能，根据采样和恢复定理，对输出的视频信号进行间距插值细分的可行性进行了论证，给出了插值细分的电路框图。分析表明其测量精度不受器件中心距大小的限制，为低位数、大中心距的固体图象传感器线阵的应用提供了方便。     

双圈拟阵

Sim■es Pereira于1992年提出双圈拟阵.本文讨论了(i)双圈拟阵及其秩函数;(ii)次模函数在双圈拟阵中的应用;(iii)双圈拟阵B(G)的横贯拟阵.主要结果:1°由圈矩阵Bf=[I,Bf12]和圈秩的概念,推出M(f0)为双圈拟阵;2°证明了双圈拟阵B(G)等于由子集族{Av∶v∈V(G)},e与v在G中相关联}所确定的横贯拟阵;3°用不同于Matthews(1977)的方法证明了(iii).     

Wavelets for multichannel signals

In this paper, we introduce and investigate multichannel wavelets, which are wavelets for vector fields, based on the concept of full rank subdivision operators. We prove that, like in the scalar and multiwavelet case, the existence of a scaling function with orthogonal integer translates guarantees the existence of a wavelet function, also with orthonormal integer translates. In this context, however, scaling functions as well as wavelets turn out to be matrix-valued functions.     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

一类新的(2n-1)点二重动态逼近细分

利用正弦函数构造了一类新的带有形状参数ω的(2n-1)点二重动态逼近细分格式.从理论上分析了随n值变化时这类细分格式的C~k连续性和支集长度;算法的一个特色是随着细分格式中参数ω的取值不同,相应生成的极限曲线的表现张力也有所不同,而且这一类算法所对应的静态算法涵盖了Chaikin,Hormann,Dyn,Daniel和Hassan的算法.文末附出大量数值实例,在给定相同的初始控制顶点,且极限曲线达到同一连续性的前提下和现有几种算法做了比较,数值实例表明这类算法生成的极限曲线更加饱满,表现力更强.     

Expression for the Number of Spanning Trees of Line Graphs of Arbitrary Connected Graphs

For any graph G, let be the number of spanning trees of G, be the line graph of G, and for any nonnegative integer r, be the graph obtained from G by replacing each edge e by a path of length connecting the two ends of e. In this article, we obtain an expression for in terms of spanning trees of G by a combinatorial approach. This result generalizes some known results on the relation between and and gives an explicit expression if G is of order and size in which s vertices are of degree 1 and the others are of degree k. Thus we prove a conjecture on for such a graph G.     

胜利断块油藏细分注水技术界限研究

老油田进入特高含水期后,剩余油分布更加零散,各种地质因素也因长期注水开发而发生了一定的改变.此时稳油控水难度进一步加大,为了进一步挖掘剩余油,控制含水上升速度、减缓产量递减,必须对注水井采取进一步的细分调整.基于水湿油藏注水井注水层段吸水效果,从注入水受力分析入手,运用达西定律推导出了水驱油藏水驱油全过程中的单位体积注入水沿竖直、地层两个方向运移的渗流速度公式,明晰了水驱油藏注水层段不同开发阶段砂岩吸水机理.研究结果表明,水驱油藏细分注水效果与岩石绝对渗透率、水相相对渗透率、注入水黏度、水动力压力梯度、注水井启动压力梯度、含水饱和度、地层倾角、油水密度差等参数有关.结合胜利油田断块油藏地质特征及细分注水工艺要求,制定了一套适合胜利油田不同断块区的细分注水技术政策界限:层段内渗透率变异系数小于0.3,砂岩条带宽度极比小于2.5,且东辛油区断块油藏层段内砂岩厚度小于6m,小层数小于4个;现河油区断块油藏层段内砂岩厚度小于5m,小层数小于5个;临盘油区断块油藏层段内砂岩厚度小于6m,小层数小于6个.矿场试验证实,该细分注水技术政策界限是合理、实用的,其为胜利断块油藏注上水、注够水、注好水,实现多层断块油藏的高效开发提供了技术保障,对类似油藏细分注水技术界限研究具有一定的借鉴意义.